Well, fine art printing in professional-grade printing shops thoroughly ensconced in the world of CMYK requires how many different inks? Just CMYK? Nope. Eighteen is the number of inks used. Just a set of CMYK inks produce in printing a very limited gamut, which is cheap-cost effective for graphics that fall within that limited gamut.
About 40% of printable colours can be achieved with CMYK inks alone. Expand to the CMYKOGV model (Cyan Magenta Yellow Black Orange Green Violet ~ also used by high-end desktop printers) and this ink set raises the colours achieved to only 72% of possible colours in printing (entire possible print gamut). Citation here
. Of course the paper type affects this gamut greatly, and the inks/application process are adjusted to accommodate this variable.
To explore this further, have a look for diagrams contrasting/comparing the gamut envelope on the hue plane
for a simple representation of the differences.
Just a couple of days ago there was a post with warm/cool in the title
. Folks took the time to explain/explore the "six primaries" there, as well.
Also, you can find a lot of interesting stuff explaining CMYK printing on the Pantone web site. Great stuff!
CMY is just a shorthand model to explain complex applications. With any model, one must learn the application limitations.